Stochastic Numerical Analysis for Impact of Heavy Alcohol Consumption on Transmission Dynamics of Gonorrhoea Epidemic

This paper aims to perform a comparison of deterministic and stochastic models. The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic model. Also, the deterministic solution is itself mean of the stochastic solution of the model. For numerical analysis, first, we developed some explicit stochastic methods, but unfortunately, they do not remain consistent in certain situations. Then we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic model. The proposed method is independent of the choice of parameters and behaves well in all scenarios. So, some theorems and simulations are presented in support of the article.     

An Effective Numerical Method for the Solution of a Stochastic Coronavirus (2019-nCovid) Pandemic Model

Nonlinear stochastic modeling plays a significant role in disciplines such as psychology, finance, physical sciences, engineering, econometrics, and biological sciences. Dynamical consistency, positivity, and boundedness are fundamental properties of stochastic modeling. A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation. Well-known explicit methods such as Euler Maruyama, stochastic Euler, and stochastic Runge–Kutta are investigated for the stochastic model. Regrettably, the above essential properties are not restored by existing methods. Hence, there is a need to construct essential properties preserving the computational method. The non-standard approach of finite difference is examined to maintain the above basic features of the stochastic model. The comparison of the results of deterministic and stochastic models is also presented. Our proposed efficient computational method well preserves the essential properties of the model. Comparison and convergence analyses of the method are presented.     

一个具有暂时免疫和非线性接触率的SIS流行病模型的分析

本文研究一个具有时滞,一般接触率,常数出生和疾病引起死亡的流行病模型.假设时滞表示暂时免疫期,即恢复者再次变成易感者所需要的时间,同时在模型中考虑了对易感者和恢复者的接种.本文得到了基本再生数R0.分析了模型的无病平衡点和地方病平衡点的存在性.通过Hurwitz准则,研究了无病平衡点和地方病平衡点的局部渐近稳定性.通过Liapunov泛函和Lasalle不变原理,证明了无病平衡点的全局渐近稳定性及在双线性接触率的情况下地方病平衡点的全局渐近稳定性.研究结果表明:R0与对易感者的有效接种率P有关,并且通过增加接种率P可以根除疾病.最后给出了数值模拟.     

随机利率情形下的多维Black-Scholes模型

利用随机微分方程和鞅方法,讨论了随机利率情形下的多维Black-Scholes定价模型,并得到随机利率情形下的欧式期权以及交换期权定价公式。     

随机潜蚤病模型的动力学行为分析

潜蚤病是贫困地区的一种人畜共患病,其发病过程极易受到随机波动环境因素的影响。因此,建立并讨论了一类以正确卫生习惯为控制策略的随机潜蚤病模型。首先,通过构造恰当的Lyapunov函数并利用It$\hat{\rm o}$公式证明了随机系统全局正解的存在唯一性。其次,在一定的条件下证明了随机系统的正解围绕在确定性系统平衡点附近的振荡行为。最后,通过数值模拟验证了理论结果的正确性。数值结果表明,当随机干扰强度足够大时将会导致疾病灭绝。     

CIR模型下保险公司最优投资再保险策略研究

本文主要研究Cox-Ingersoll-Ross（CIR）随机利率模型下保险公司的最优投资和再保险问题．假设保险公司投资于金融市场中的无风险资产、零息债券和多种股票．此外保险公司购买比例再保险合约以转移承保风险．模型中,我们用仿射过程刻画随机利率,通过扩散过程模拟保险公司盈余过程,即用连续过程近似跳过程．保险公司的目标是通过保险投资最大化终端财富的期望幂效用．由于保险公司的财富过程不是自融资过程,在求解过程中,我们先将原优化问题转化为自融资问题,通过随机最优控制方法导出相应的HJB方程,进而得到最优投资、再保险策略和幂效用函数下的最优值函数．我们发现随着风险厌恶系数的增大,公司投资于股票的比例会降低,初始利率越高,保险公司终端财富的值函数越大．最后,我们给出了保费率、利率参数和风险厌恶系数对投资策略、投资效用的敏感性分析．     

具有非线性传染率的两类传染病模型的全局分析

讨论了两类带有非线性传染率的SIS型和SIRS型传染病模型,得到了各类平衡点存在的阈值条件。借助构造Dulac函数和Liapunov函数,找到了各类平衡点全局渐近稳定的充要条件。     

Prediction-Correction Scheme for Decoupled Forward Backward Stochastic Differential Equations with Jumps

By introducing a new Gaussian process and a new compensated Poisson random measure, we propose an explicit prediction-correction scheme for solving decoupled forward backward stochastic differential equations with jumps (FBSDEJs). For this scheme, we first theoretically obtain a general error estimate result, which implies that the scheme is stable. Then using this result, we rigorously prove that the accuracy of the explicit scheme can be of second order. Finally, we carry out some numerical experiments to verify our theoretical results.     

一类具有非线性发生率的SEIR传染病模型的全局稳定性分析

本文对一类具有非线性发生率的SEIR传染病模型进行了研究.确定了决定疾病灭绝或持续存在的阈值-基本再生数,并分析了模型的平衡点的存在性;通过构造恰当的Lyapunov函数,运用La Salle不变性原理证明了当基本再生数小于或等于1时,无病平衡点是全局渐进稳定的;利用Lyapunov直接方法证明了当基本再生数大于1时,地方病平衡点是全局渐进稳定的.最后,将发生率具体化用数值模拟验证了所得理论分析结果的正确性.     

随机调幅Rattling振动的二级传动模型

迫击 (Rattling)振动是汽车齿轮传动中不期望产生的振动 ,它是由于齿轮传动过程中在空载作用下产生的 ,目前已得到许多专家与学者的关注。本文研究随机调幅二级传动的 Rattling振动 ,直接采用非高斯截断技术 ,导出一个用平均映射描述的离散随机模型 ,并通过平均庞加莱图和平均速度的功率谱密度揭示随机调幅 Rattling振动的二级传动随机模型的性质 ,同时通过最大李雅普诺夫指数给出混沌发生的参数域。     

一类具有饱和传染率且带有潜伏期和接种期的SVEIR模型的研究

本文研究了带有潜伏期和接种期的传染病,建立一类具有饱和发生率且带有潜伏期和接种期的SVEIR模型,找到了决定疾病绝灭或持续生存的阀值―基本再生数.通过构造合适的Lyapunov函数,运用LaSalle不变集原理,证明了当基本再生数小于1时,无病平衡点是全局渐近稳定的;当基本再生数大于1时,存在唯一的感染平衡点,并且得到了该平衡点的全局稳定性.最后,数值模拟验证了理论的正确性.     

Logistic增长的时滞SIS模型分析

本文研究了一类具有生理阶段结构的Logistic增长的SIS传染病模型,给出了系统边界平衡点和正平衡点全局渐近稳定的条件。即得到了传染病最终消除和成为地方病的阈值。     

变时滞随机微分方程的指数稳定性

通过构建李雅普偌夫函数和利用半鞅收敛定理,对一类随机变时滞微分方程的全局指数稳定进行了分析,提出了易于判定随机变时滞微分方程几乎必然指数稳定件新的代数判据,推广了现有文献中的主要结论,并给出实例加以验证。     

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

The goal of this research is to introduce the simulation studies of the vector-host disease nonlinear system (VHDNS) along with the numerical treatment of artificial neural networks (ANNs) techniques supported by Levenberg-Marquardt backpropagation (LMQBP), known as ANNs-LMQBP. This mechanism is physically appropriate, where the number of infected people is increasing along with the limited health services. Furthermore, the biological effects have fading memories and exhibit transition behavior. Initially, the model is developed by considering the two and three categories for the humans and the vector species. The VHDNS is constructed with five classes, susceptible humans , infected humans , recovered humans , infected vectors , and susceptible vector based system of the fractional-order nonlinear ordinary differential equations. To solve the number of variations of the VHDNS, the numerical simulations are performed using the stochastic ANNs-LMQBP. The achieved numerical solutions for solving the VHDNS using the stochastic ANNs-LMQBP have been described for training, verifying, and testing data to decrease the mean square error (MSE). An extensive analysis is provided using the correlation studies, MSE, error histograms (EHs), state transitions (STs), and regression to observe the accuracy, efficiency, expertise, and aptitude of the computing ANNs-LMQBP.     

随机局部弹性与分批连续进货的随机存储模型

利用随机局部弹性的概念及运算法则,研究了分批连续进货并允许缺货的存储模型中,总费用对随机最高存储量与随机采购周期的局部弹性,给出了总费用弹性的联合概率密度的一般表达式,通过实例证明了当最高存储量与采购周期的分布特性已知时,总费用的弹性分布和弹性变化范围及弹性在该变化范围的可信度。     

Dynamical Behavior and Sensitivity Analysis of a Delayed Coronavirus Epidemic Model

Mathematical delay modelling has a significant role in the different disciplines such as behavioural, social, physical, biological engineering, and bio-mathematical sciences. The present work describes mathematical formulation for the transmission mechanism of a novel coronavirus (COVID-19). Due to the unavailability of vaccines for the coronavirus worldwide, delay factors such as social distance, quarantine, travel restrictions, extended holidays, hospitalization, and isolation have contributed to controlling the coronavirus epidemic. We have analysed the reproduction number and its sensitivity to parameters. If,     

Structure Preserving Algorithm for Fractional Order Mathematical Model of COVID-19

In this article, a brief biological structure and some basic properties of COVID-19 are described. A classical integer order model is modified and converted into a fractional order model with as order of the fractional derivative. Moreover, a valued structure preserving the numerical design, coined as Grunwald–Letnikov non-standard finite difference scheme, is developed for the fractional COVID-19 model. Taking into account the importance of the positivity and boundedness of the state variables, some productive results have been proved to ensure these essential features. Stability of the model at a corona free and a corona existing equilibrium points is investigated on the basis of Eigen values. The Routh–Hurwitz criterion is applied for the local stability analysis. An appropriate example with fitted and estimated set of parametric values is presented for the simulations. Graphical solutions are displayed for the chosen values of (fractional order of the derivatives). The role of quarantined policy is also determined gradually to highlight its significance and relevancy in controlling infectious diseases. In the end, outcomes of the study are presented.